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Simplifying 80x + -4x2 = 10 Solving 80x + -4x2 = 10 Solving for variable 'x'. Reorder the terms: -10 + 80x + -4x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 80x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 40x + -2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + 40x + -2x2)' equal to zero and attempt to solve: Simplifying -5 + 40x + -2x2 = 0 Solving -5 + 40x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 2.5 + -20x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -20x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -20x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -20x + x2 = 0 + -2.5 -20x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -20x + x2 = -2.5 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = -2.5 + 100 Reorder the terms: 100 + -20x + x2 = -2.5 + 100 Combine like terms: -2.5 + 100 = 97.5 100 + -20x + x2 = 97.5 Factor a perfect square on the left side: (x + -10)(x + -10) = 97.5 Calculate the square root of the right side: 9.874208829 Break this problem into two subproblems by setting (x + -10) equal to 9.874208829 and -9.874208829.Subproblem 1
x + -10 = 9.874208829 Simplifying x + -10 = 9.874208829 Reorder the terms: -10 + x = 9.874208829 Solving -10 + x = 9.874208829 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 9.874208829 + 10 Combine like terms: -10 + 10 = 0 0 + x = 9.874208829 + 10 x = 9.874208829 + 10 Combine like terms: 9.874208829 + 10 = 19.874208829 x = 19.874208829 Simplifying x = 19.874208829Subproblem 2
x + -10 = -9.874208829 Simplifying x + -10 = -9.874208829 Reorder the terms: -10 + x = -9.874208829 Solving -10 + x = -9.874208829 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -9.874208829 + 10 Combine like terms: -10 + 10 = 0 0 + x = -9.874208829 + 10 x = -9.874208829 + 10 Combine like terms: -9.874208829 + 10 = 0.125791171 x = 0.125791171 Simplifying x = 0.125791171Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.874208829, 0.125791171}Solution
x = {19.874208829, 0.125791171}
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